However, our build computer does not (no development takes place on it).

Today, our part of the product prevented a global build from completing successfully.

By trial and error, we discovered that it was caused by the licence.licx files. We found that if they are all EMPTY on the build computer, it builds successfully. We then learned that one of our developers had checked in one of his licence.licx files which contained token keys (written automatically, it seems).

My question is: What is the correct way to handle these licence.licx files on a build computer without an Infragistics licence?

So far, ensuring they exist but remain empty works for us, but an internet search turned up a mix of suggestions, including setting the Build Action in VS's (2010 in our case) File Properties to "None". We have it set to "Embedded Resource", which seems to be the default.

The Building Apps Using NetAdvantage with Team Build blog post covers using a separate server for building. Davide is also correct that having an empty licenses.licx file will allow you to build and that you still do need to have a license to be in compliance with the license agreement.